How to find that three linear equation has no solution?
Answers
You are probably familiar with linear equations, such as y = 3x + 4 or y - 3x = 4. These equations, when graphed, will give you a straight line. A linear system, then, is a collection of linear equations. Our usual linear equations have only two variables. Because we have two variables, a linear system using these kinds of equations will have two equations.
But, did you know that you can also have a linear system with three variables? Yes, you can. A linear system in three variables, then, will have three equations since it has three variables. These equations, just like the ones with only two variables, will not have any exponents. This is an example of a linear system in three variables:
Three variable linear system
three variable linear system
Looking at this system, we see our three variables, x, y, and z. These three letters are the most commonly used, although you can use any letter that you want; they don't have to be in order, either. If you have a friend named Sam, you could easily use those three letters, too. The important thing to remember is that we have three different variables, and none of them have exponents with them.
You will see these kinds of linear systems in higher math, where you will be asked to solve them. Just like other systems, our linear system in three variables can have one solution, no solution, or an infinite number of solutions. Just like the other equations that we are used to solving, if our system has only one solution, then we look for just one point. But, what about the other two? How do you find out if our system has no solution or an infinite number of solutions? Let's find out.
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